Reduced Order Modeling of Reactive Transport in a Column

Background

It is estimated that approximately 93% of the earth's available fresh water supply is stored underground. The fate of solutes that contaminate this source of fresh water are a matter of serious concern.

Computational modeling aids understanding of solute fate in the subsurface environment, where direct observation is difficult or impossible. This modeling of reactive contaminant transport systems can be a computationally demanding task, requiring the computation of many thousands of unknown coefficients at every time step using standard methods (i.e.,finite difference, finite element). This is compounded in settings such as parameter estimation, when a simulation must be repeated many times with parameters that vary in a given range.

We create a reduced order model to approximate the solution of a system of reactive transport equations with a decreased number of unknown coefficients. We show that the reduced model is able to approximate the high-order finite element model.